In the triangle ABC, the angle C is equal to 112 “, the biccetrices of the angles A and B intersect

In the triangle ABC, the angle C is equal to 112 “, the biccetrices of the angles A and B intersect at the point O. Find the degree measure of the angle AOB.

Since the sum of the angles of a triangle is 180 °, then the sum of the angles A and B will be:

180 – 112 = 68 °.

Since AO and BO are bisectors, the sum of the angles OAB OBA is:

OAB + OBA = 1/2 * (A + B) = 1/2 * 68 = 34 °.

From triangle AOB we get:

AOB = 180 – 34 = 146 °.

Answer: the desired angle is 146 °.